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Symbols
d: depth of tee or width of web leg A: cross-sectional area of angle, in.2 (mm2)
b: width of leg, in. (mm)
Cb: The lateral-torsional buckling modification factor
E: Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
Fy: Specified minimum yield stress of the type of steel being used, ksi
h: Distance as defined in AISC 360-16 Table 4.1b
Lb: Length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross-section, in. (mm)
Lp: The limiting laterally unbraced length for the limit state of yielding, in. (mm)
Lr: The limiting unbraced length for the limit state of inelastic Mcr: The elastic lateral-torsional buckling , in. (mm),moment
Mn: The nominal flexural strength
Mp: Plastic bending moment
My: Yield moment about the axis of bending, kip-in. (N-mm)
Sxc: elastic section modulus , in.3 (mm3)
Sxc: elastic section modulus referred to the compression flangeto the toe in compression relative to the bending axis, in.3 (mm3)
Sy: elastic section modulus taken about the y-axis, in.3 (mm3)
tf: the thickness of the flangeangle leg, in. (mm)
Zy = Plastic section modulus about the y-βw: section property for single angles about major principal axis, in. 3 (mm3)
λp: Limiting slenderness for a compact flange, defined in Table B4.1b
λr: Limiting slenderness for a noncompact flange, described in Table B4.1b
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The nominal flexural strength, Mn, should be the lower value obtained according to the limit states of yielding (plastic moment), lateral torsional buckling, flange local buckling, and leg local buckling of tee stems and double-angle web legs.
The nominal flexural strength of single-angle members is calculated by considering the geometric axis and principal-es cross-sectional properties. Only the limit states of yielding and leg local buckling apply for bending about the minor principal axis.
Yielding Limit State
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Lateral Torsional Buckling Limit State
The nominal flexural strength, M
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n, for single angles without continuous lateral-torsional restraint along the length is calculated as shown below.
Mathinline body --uriencoded--$$ \normalsize
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\mathrm%7BWhen%7D \;\; \
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dfrac%7BM_y%7D%7BM_%7Bcr%7D%7D \le 1.0 \; \;\;\;\;\;\;\;\;\;\;
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M
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The plastic bending moment, Mp, for tee, stems in compression is calculated as shown below.
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The plastic bending moment, Mp, for double angles with web legs in compression is calculated as shown below.
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_%7Bn%7D = \Bigg( 1.92-1.17 \sqrt%7B\dfrac%7BM_y%7D%7BM_%7Bcr%7D%7D%7D \Bigg)M_y \le 1.5 M_y \; \;\;\;\;\;\;\;\;\;\;\;\;\;
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Lateral Torsional Buckling Limit State
The lateral torsional buckling limit state is calculated for stems and web legs in tension.
When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply.
When Lp < Lb ≤ Lr
(F10-2) $$ Mathinline body --uriencoded--$$ \normalsize
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\mathrm%7BWhen%7D \;\; \dfrac%7BM_y%7D%7BM_%7Bcr%7D%7D > 1.0 \; \;\;\;\;\;\;\;\;\;\;
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When Lb > Lr
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Limiting laterally unbraced length for the limit state of yielding, Lp is calculated as shown below.
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M_%7Bn%7D = \Bigg( 0.92-\dfrac%7B0.17M_%7Bcr%7D%7D%7BM_%7By%7D%7D \Bigg)M_y \; \;\;\;\;\;\;\;\;\;\;\;\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;
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(F10-3) $$
The elastic lateral-torsional buckling , Lr moment, Mcr, for bending about the major principal axis of single angles is calculated as shown below.
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The elastic lateral-torsional buckling moment, Mcr, for bending about one of the geometric axes of an equal leg angle with no axial compression of single angles is calculated as shown below.
With no lateral-torsional restraint:
With maximum compression at the toe, Mcr is calculated as shown below.
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where
d: depth of tee or width of web leg in tension, in. (mm)
For tee stems and web legs in compression, the elastic lateral-torsional buckling moment, Mcr, and The nominal flexural strength, Mn, are calculated below.
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With maximum tension at the toe, Mcr is calculated as shown below.
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where
d: depth of tee or width of web leg in compression, in. (mm)
The nominal flexural strength, Mn, is calculated for double-angle web legs given the title.
Flange Local Buckling Limit State of Tees and Double-Angle LegsMy should be taken as 0.80 times the yield moment calculated using the geometric section modulus.
With lateral-torsional restraint at the point of maximum moment only:
The elastic lateral-torsional buckling moment, Mcr, is calculated as 1.25 times Mcr computed using Equations F10-5a or F10-5b. My should be calculated using the geometric section modulus as the yield moment.
Leg Local Buckling Limit State
The limit state of flange leg local buckling does not apply for tee flange sections when the toe of the leg is in compression with compact flanges section in flexural compression.
The nominal flexural strength, Mn Mn, is calculated as shown below for tee flange sections with noncompact flanges in flexural compression. legs
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The nominal flexural strength, Mn Mn, is calculated as shown below for tee flange sections with slender flanges in flexural compression.
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legs
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Local Buckling Limit State of Tee Stems and Double-Angle Web Legs in Flexural Compression
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The nominal flexural strength, Mn, is calculated for double-angle web legs given the title.
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